Scattering-matrix formulation of curved-wave multiple-scattering theory: Application to x-ray-absorption fine structure

Curved-wave multiple-scattering contributions to XAFS (x-ray-absorption fine structure) are calculated with use of an efficient formalism similar to that based on the plane-wave approximation, but with scattering amplitudes f () replaced by distance-dependent ``scattering matrices'' F, ' (, '). Here =kR, k being the photoelectron wave number and R is a bond vector, while the matrix indices = (, ) represent terms in a convergent expansion that generalizes the small-atom approximation. This approach is based on an exact, separable representation of the free propagator (or translation operator) matrix elements, G₋, ₋' (kR), in an angular momentum L= (l, m) and site basis. The method yields accurate curved-wave contributions for arbitrarily high-order multiple-scattering paths at all positive energies, including the near-edge region. Results are nearly converged when the intermediate summations are truncated at just six terms, i. e. , (66) matrices. The lowest-order (11) matrix F₀₀, ₀₀ is the effective, curved-wave scattering amplitude, f (, ', ), and yields a multiple-scattering expansion equivalent to the point-scattering approximation. Formulas for multiple-scattering contributions to XAFS and photoelectron diffraction are presented, and the method is illustrated with results for selected multiple-scattering paths in fcc Cu.